Constructing (Bi)Similar Finite State Abstractions using Asynchronous ll-Complete Approximations

This paper constructs a finite state abstraction of a possibly continuous-time and infinite state model in two steps. First, a finite external signal space is added, generating a so called $\Phi$-dynamical system. Secondly, the strongest asynchronous $l$-complete approximation of the external dynamics is constructed. As our main results, we show that (i) the abstraction simulates the original system, and (ii) bisimilarity between the original system and its abstraction holds, if and only if the original system is $l$-complete and its state space satisfies an additional property

Comparing Asynchronous ll-Complete Approximations and Quotient Based Abstractions

This paper is concerned with a detailed comparison of two different abstraction techniques for the construction of finite state symbolic models for controller synthesis of hybrid systems. Namely, we compare quotient based abstractions (QBA), with different realizations of strongest (asynchronous) $l$-complete approximations (SAlCA) Even though the idea behind their construction is very similar, we show that they are generally incomparable both in terms of behavioral inclusion and similarity relations. We therefore derive necessary and sufficient conditions for QBA to coincide with particular realizations of SAlCA. Depending on the original system, either QBA or SAlCA can be a tighter abstraction

Discrete supervisory control of hybrid systems based on l- complete approximations

The topic of this paper is the synthesis of discrete supervisory control for hybrid systems Sigma with discrete external signals. Such systems are in general neither l- complete nor can they be represented by finite state machines. Our solution to the control problem is as follows: we find the strongest l-complete approximation (abstraction) Sigma (l) for Sigma, represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists on the approximation level, we synthesize the maximally permissive supervisor for Sigma (l). We show that it also solves the control problem for the underlying hybrid system Sigma. If no solution exists, approximation accuracy can be increased by computing the strongest k-complete abstraction Sigma (k), k > l. The basic ideas regarding the approximation step are explained within the framework of Willems' behavioral systems theory. Implementation issues are treated in a state space framework, and the main results are interpreted from a traditional control engineering point of view. copyright 2002 Kluwer Academic Publishers [accessed 2014 April 1st

Discrete supervisory control of hybrid systems based on l- complete approximations

The topic of this paper is the synthesis of discrete supervisory control for hybrid systems Sigma with discrete external signals. Such systems are in general neither l- complete nor can they be represented by finite state machines. Our solution to the control problem is as follows: we find the strongest l-complete approximation (abstraction) Sigma (l) for Sigma, represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists on the approximation level, we synthesize the maximally permissive supervisor for Sigma (l). We show that it also solves the control problem for the underlying hybrid system Sigma. If no solution exists, approximation accuracy can be increased by computing the strongest k-complete abstraction Sigma (k), k > l. The basic ideas regarding the approximation step are explained within the framework of Willems' behavioral systems theory. Implementation issues are treated in a state space framework, and the main results are interpreted from a traditional control engineering point of view

Correct-By-Construction Fault-Tolerant Control

Correct-by-construction control synthesis methods refer to a collection of model-based techniques to algorithmically generate controllers/strategies that make the systems satisfy some formal specifications. Such techniques attract much attention as they provide formal guarantees on the correctness of cyber-physical systems, where corner cases may arise due to the interaction among different modules. The controllers synthesized through such methods, however, may still malfunction due to faults, such as physical component failures and unexpected operating conditions, which lead to a sudden change of the system model. In these cases, we want to guarantee that the performance of the faulty system degrades gracefully, and hence achieve fault tolerance. This thesis is about 1) incorporating fault detection and detectability analysis algorithms in correct-by-construction control synthesis, 2) formalizing the graceful degradation specification for fault tolerant systems with temporal logic, and 3) developing algorithms to synthesize correct-by-construction controllers that achieve such graceful degradation, with possible delay in the fault detection. In particular, two sets of approaches from the temporal logic planning domain, i.e., abstraction-based synthesis and optimization-based path planning, are considered. First, for abstraction-based approaches, we propose a recursive algorithm to reduce the fault tolerant controller synthesis problem into multiple small synthesis problems with simpler specifications. Such recursive reduction leverages the structure of the fault propagation and hence avoids the high complexity of solving the problem monolithically as one general temporal logic game. Furthermore, by exploring the structural properties in the specifications, we show that, even when the fault is detected with delay, the problem can be solved by a similar recursive algorithm without constructing the belief space. Secondly, optimization-based path planning is considered. The proposed approach leverages the recently developed temporal logic encodings and state-of-art mixed integer programming (MIP) solvers. The novelty of this work is to enhance the open-loop strategy obtained through solving the MIP so that it can react contingently to faults and disturbance. Finally, the control synthesis techniques developed for discrete state systems is shown to be applicable to continuous states systems. This is demonstrated by fuel cell thermal management application. Particularly, to apply the abstraction-based synthesis methods to complex systems such as the fuel cell thermal management system, structural properties (e.g., mixed monotonicity) of the system are explored and leveraged to ease abstraction computation, and techniques are developed to improve the scalability of synthesis process whenever the system has a large number of control actions.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155031/1/yliren_1.pd